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Chap006

# Chap006 - C hapter 6 D iscounted Cash F low Valuation...

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Chapter 6 Discounted Cash Flow Valuation

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Multiple Cash Flows-FV Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years? FV = 500(1.09) 2 + 600(1.09) = 1248.05 Year 0 CF: 2 N; -500 PV; 9 I/Y; CPT FV = 594.05 Year 1 CF: 1 N; -600 PV; 9 I/Y; CPT FV = 654.00 Total FV = 594.05 + 654.00 = 1248.05 Sometimes, doing the arithmetic is quicker than using the function keys.
Multiple Cash Flows – PV You are considering an investment that will pay you \$1000 in one year, \$2000 in two years and \$3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay? PV = 1000 / (1.1) 1 = 909.09 N = 1; I/Y = 10; FV = 1000; CPT PV = -909.09 PV = 2000 / (1.1) 2 = 1652.89 N = 2; I/Y = 10; FV = 2000; CPT PV = -1652.89 PV = 3000 / (1.1) 3 = 2253.94 N = 3; I/Y = 10; FV = 3000; CPT PV = -2253.94 PV = 909.09 + 1652.89 + 2253.94 = 4815.92

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Annuities and Perpetuities Defined Annuity – finite series of equal payments that occur at regular intervals If the first payment occurs at the end of the period, it is called an ordinary annuity We assume all problems are solved in this way unless told otherwise; default calculator setting If the first payment occurs at the beginning of the period, it is called an annuity due Perpetuity – infinite series of equal payments
Annuities and Perpetuities – Basic Formulas Perpetuity: PV = C / r Annuities: periods. of number the is t and rate interest the is r flow, cash annuity the is C where 1 Factor Value Future 1 ) 1 ( r Factor Value Present 1 ) 1 ( 1 1 - = - + = - = + - = r C r r C FVA C r r C PVA t t

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Annuity Notation The present value factor is sometimes called the PVIFA—Present Value Interest Factor for Annuities, and written as PVIFA(r,t). Think of it as the present value of \$1 discounted back t periods at a rate r. Example: The present value of \$500 received 3 years from now, if r=10% is: I will not use the PVIFA notation in class, but the solutions manual uses it occasionally. t r ) 1 ( 1 + \$375.66 3) , 10 (. * 500 ) 10 . 1 ( 500 \$ 3 = = + PVIFA
Annuities and the Calculator You can use the PMT key on the calculator for the equal payment The sign convention still holds Ordinary annuity versus annuity due You can switch your calculator between the two types by hitting <2 nd > <PMT>, then <2 nd > <ENTER> on the TI BA-II Plus If you see “BGN” in the upper right corner of your calculator display, you have it set for an annuity due Don’t forget to switch back to “END” when finished by repeating the above process.

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Annuity – Using the PMT key Suppose you win the Publishers Clearinghouse \$10 million sweepstakes. The money is paid in equal annual installments of \$333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?
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Chap006 - C hapter 6 D iscounted Cash F low Valuation...

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